Block #500,185

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 12:45:20 AM · Difficulty 10.7974 · 6,314,203 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

756d91b7e52919b668d49f7abb3f4df02c4b5a1a056216b51c250de36776afdd

View on Chainz ↗

Height

#500,185

Difficulty

10.797396

Transactions

Size

639 B

Version

Bits

0acc221e

Nonce

1,504,255,648

Timestamp

4/19/2014, 12:45:20 AM

Confirmations

6,314,203

Mined by

⛏️ P2SHASvPXhLSqDaejxRvmXwmv8scXCa6QhtmR7

Merkle Root

af6c25f1800a7e4c966cbf9a4eb9559ce994b2989a914070c5b71d27db4558d2

Transactions (2)

Coinbasef4d7fcfe4cff05…1e25275e744c93

1 in → 1 out8.5700 XPM109 B

ASvPXhLS…a6QhtmR7

f6af2351433406…7f83efea3f4c12

2 in → 6 out17.2700 XPM441 B

AdGV3q2y…E8KneMBo AeKNrjNj…1NEq95Ta Acq7Tfk5…5zvD82s5 AW9UAps1…PoAQ39bN AHbu8w6V…13P7BwSQ

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.073 × 10⁹²(93-digit number)

20731482644828085683…52986639430022649499

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.073 × 10⁹²(93-digit number)

20731482644828085683…52986639430022649499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.073 × 10⁹²(93-digit number)

20731482644828085683…52986639430022649501

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.146 × 10⁹²(93-digit number)

41462965289656171366…05973278860045298999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.146 × 10⁹²(93-digit number)

41462965289656171366…05973278860045299001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.292 × 10⁹²(93-digit number)

82925930579312342732…11946557720090597999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.292 × 10⁹²(93-digit number)

82925930579312342732…11946557720090598001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.658 × 10⁹³(94-digit number)

16585186115862468546…23893115440181195999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.658 × 10⁹³(94-digit number)

16585186115862468546…23893115440181196001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.317 × 10⁹³(94-digit number)

33170372231724937092…47786230880362391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.317 × 10⁹³(94-digit number)

33170372231724937092…47786230880362392001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #500,185

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